We characterise the class SRaCAn of subalgebras of relation algebra reducts of n-dimensional cylindric algebras (for finite n 5) by the notion of a `hyper-basis', analogous to the cylindric basis of Maddux, and by relativised representations. A corollary is that SRaCAn = SRa(CAn " Crs n) = SRa(CAn " Gn). We outline a game-theoretic approximation to the existence of a representation, and how to use it to obtain a recursive axiomatisation of SRaCAn.
|
145
|
Boolean algebras with operators
– J'onsson, Tarski
- 1951
|
|
94
|
A Formalization of Set Theory without Variables
– Tarski, Givant
- 1987
|
|
69
|
Cylindric Algebras (Part I
– Henkin, Monk, et al.
- 1971
|
|
67
|
Model theory, Encyclopedia of Mathematics and
– Hodges
- 1993
|
|
60
|
Infinitary logic and inductive definability over finite structures
– Dawar, Lindell, et al.
- 1995
|
|
60
|
The representation of relational algebras
– Lyndon
- 1950
|
|
46
|
Topics in relation algebra
– Maddux
- 1978
|
|
44
|
On representable relation algebras
– Monk
- 1964
|
|
42
|
Some varieties containing relation algebras
– Maddux
- 1982
|
|
42
|
The origin of relation algebras in the development and axiomatization of the calculus of relations
– Maddux
- 1991
|
|
29
|
Step by step --- building representations in algebraic logic
– Hirsch, Hodkinson
- 1997
|
|
29
|
Algebraic Logic
– Andréka, Németi, et al.
- 2001
|
|
23
|
Representation Problems for Relation Algebras
– J'onsson, Tarski
- 1948
|
|
21
|
Introductory course on relation algebras, finitedimensional cylindric algebras, and their interconnections
– Maddux
- 1991
|
|
20
|
Finite algebras of relations are representable on finite sets
– Andr'eka, Hodkinson, et al.
- 1999
|
|
19
|
Non-finite axiomatizability results for cylindric and relation algebras
– Maddux
- 1989
|
|
19
|
Nonfinitizability of classes of representable cylindric algebras
– Monk
- 1969
|
|
17
|
Complete representations in algebraic logic
– Hirsch, Hodkinson
- 1997
|
|
14
|
Relation algebras and projective geometries
– Lyndon
- 1961
|
|
13
|
A sequent calculus for relation algebras
– Maddux
- 1983
|
|
12
|
Representability is not decidable for finite relation algebras
– Hirsch, Hodkinson
- 1999
|
|
11
|
Relation algebras with n-dimensional relational bases
– Hirsch, Hodkinson
- 1997
|
|
10
|
Sur l'extension aux relations de quelques propri'et'es des ordres
– Fraiss'e
- 1954
|
|
10
|
Axiomatising various classes of relation and cylindric algebras
– Hirsch, Hodkinson
- 1997
|
|
10
|
The representation of relation algebras
– McKenzie
- 1966
|
|
8
|
Relation algebra reducts of cylindric algebras and an application to proof theory
– Hirsch, Hodkinson, et al.
- 1998
|
|
8
|
Complete Description of Substitutions in Cylindric Algebras and other Algebraic Logics
– Thompson
- 1993
|
|
6
|
Relation algebras of every dimension
– Maddux
- 1992
|
|
5
|
A Stone type representation theorem for algebras of relations of higher rank
– Andr'eka, Thompson
- 1988
|
|
3
|
Model theory, volume 42 of Encylopedia of mathematics and its applications
– Hodges
- 1993
|
|
3
|
Axiomatizing complex algebras by games
– Mikul'as, Venema
- 1999
|
|
3
|
Defining relations for full semigroups of finite transformations
– J'onsson
- 1962
|
|
2
|
generators in finite full transformation semigroups
– Howie
- 1978
|
|
2
|
Finite axiomatizability of SNr n CA n+1 and non-finite axiomatizability of SNr n CA n+2 . Lecture notes for a series of lectures given at the Algebraic Logic Meeting
– Andreka
- 1990
|
|
2
|
Complexity of equations valid in algebras of relations. Annals of Pure and Applied Logic
– Andreka
- 1998
|
|
2
|
Relation algebras with n-dimensional bases. submitted to Annals of Pure and Applied Logic
– Hirsch, Hodkinson
- 1998
|
|
2
|
On the number of variables required
– Hirsch, Hodkinson, et al.
- 1998
|
|
1
|
On the representation theory for cylindric algebras
– Monk
- 1961
|
|
1
|
The Workload for the SPECweb96 Benchmark. URL http://www.sepcbench.org/osg/web96/workload.html This article was processed using the L scaled 913a T E X macro package with LLNCS style
– unknown authors
- 1999
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